Introduction
What are Linear Mixed Effects Models (LMMs)?
This type of model is increasingly common in the analysis of biological data. Utilized when complex data structures demand methods beyond simple analysis. It is an extension of traditional linear models that incorporates fixed and random effects.
What are fixed and random effects?
Fixed Effects: Standard predictor variables, specific comparisons, and measured all levels of interest
Random Effects: typically represent a grouping variable. Allows researchers to look at specific levels found in the study as a small part of a larger population.
What two things may happen if estimates of variance of intercept terms if less than 5 levels are used?
-The variance estimate will collapse to Zero
or
- The variance will be non-zero but likely incorrect
This type of linear model, previously discussed in class can be applied to LMMs to account for heteroscedasticity in place of a transformation.
Generalized linear model; or Generalized linear mixed model
How do random effects reduce type 1 and type 2 errors?
Random effects usually indicate a grouping variable and enable the estimation of variance in the response variable both within and between these groups.
What is the importance of random effects, what is shrinkage, and how does it relate to random effects?
They accurately reflect messy ecological reality if done correctly, are fantastic at handling non-independence, and have the ability to predict unmeasured groups.
Shrinkage is an idea that the estimated means of the group drift towards the global means. Random effects use the data from all groups to estimate the mean, and because the model assumes all group means are drawn from this common distribution, the individual estimates of the group means are shrunk toward the global mean
This common statistic is ill-advised for unbalanced experimental designs and irrelevant for non-Gaussian error structures.
What is an F-test?
How do crossed and nested factor experimental designs affect the interpretability of factor interactions?
-Crossed factors allow the model to estimate the interaction effects between the two accurately
-Nested factors automatically pool those effects into he second factor
Why is it important to use LMMs correctly in the biological science setting, and why is it challenging?
Importance: Provide robust and accurate biological inferences, address complex ecological data settings, and enable advanced analysis.
Challenges:
1. They make additional assumptions about the data beyond those made in more standard statistical techniques, such as general linear models
2. Interpreting model output correctly can be challenging, especially for the variance components of random effects
3. Certain standard statistical tests used for model comparison do not perform reliably when applied to models that include random effects
How do random effects allow for the control of non-independence? What happens when fitting a random intercept, and what happens when both random intercept and slope are fitted?
They constrain non-independent 'units' to have the same intercept and/or slope.
Fitting only a random intercept allows the group means to vary, but assumes all groups have a common slope for a fitted covariate (fixed effect).
Fitting both random intercept and slopes allows the slope of a predictor to vary based on separate grouping variables.
Describe two ways in which you may miss-specify randoms effects (either from the paper or not)
- (i) failure to recognize non-independence caused by nested structures in the data
- (ii) failing to specify random slopes to prevent constraining slopes of predictors to be identical across clusters in the data
- (iii) testing the significance of fixed effects at the wrong ‘level’ of hierarchical models that ultimately leads to pseudoreplication and inflated Type I error rates
What is the best way to avoid 'fishing expeditions'? I.E, what is the best way to maximize the odds that your LMM is reliable and meaningful?
A-priori considerations. Consider your linear mixed model in your experimental design; consider sample sizes, measurements, data structure... Use your head!